Question

Natural numbers 1 to 25 (both inclusive) are split into 5 groups of 5 numbers each. The medians of these 5 groups are A, B, C, D and E. If the average of these medians is m, what are the smallest and the largest values m can take?

• A. 9, 17
• B. 7, 18
• C. 8, 18
• D. 5, 20

Answer 1

The correct option is A 9, 17

To get the maximum possible value for m, we have to group the numbers similar to this: (1,2,23,24,25), (3,4,20,21,22), (5,6,17,18,19), (7,8,14,15,16) and (9,10,11,12,13) A, B, C, D and E are 23, 20, 17, 14, and 11. So, m will be 17
To get the minimum value, we’ll again have to rearrange like following: (1,2,3,24,25), (4,5,6,22,23), (7,8,9,20,21), (10,11,12,18,19) and (13,14,15,16,17) A, B, C, D and E will be 3, 6, 9, 12 and 15. So, m will be 9.